INTEGRAL_FLUX
  ! 2 x 2 x - with the connection between 1 and 5 carved out: 3 total
  ! 3 m^2 \perp Z
  ! @ 1 mm/s for 2 s = -6 kg total, -3 kg/s
  NAME Z3
  INVERT_DIRECTION
  POLYGON
    1. 0. 1.
    2. 0. 1.
    2. 2. 1.
    0. 2. 1.
    0. 1. 1.
    1. 1. 1.
  /
END

INTEGRAL_FLUX
  ! 2 x 1 x - top
  ! 2 m^2 \perp Z
  ! @ 1 mm/s for 2 s = 4 kg total, 2 kg/s
  NAME top
  POLYGON
    0. 0. 2.
    2. 1. 2.
  /
END

INTEGRAL_FLUX
  NAME entire_top
  ! 4 m^2 \perp Z
  ! @ 1 mm/s for 2 s = 8 kg total, 4 kg/s
  PLANE
    0. 0. 2.
    1. 0. 2.
    0. 1. 2.
  /
END

# coordinates and directions
INTEGRAL_FLUX
  ! 1 m^2 \perp X, Y, Z = 3 m^2 total
  ! @ 1 mm/s for 2 s = -2 kg total, -1 kg/s
  ! negative due to -0.5 direction in z
  NAME top_north_east_corner_z
  COORDINATES_AND_DIRECTIONS
    1.5 1.5 2. 0. 0. -0.5  ! top face of cell 8
  /
END

# =============================== Z plane at 0 ================================
INTEGRAL_FLUX
  ! @ 1 mm/s for 2 s = 8 kg total, 4 kg/s
  NAME Z_at_0
  VERTICES
    4 5 2 1
    5 6 3 2
    7 8 5 4
    8 9 6 5
  /
END

! the four below should sum to the above
INTEGRAL_FLUX Z_at_0_1
  VERTICES
    1 2 5 4
  /
END

INTEGRAL_FLUX Z_at_0_2
  VERTICES
    2 3 6 5
  /
END

INTEGRAL_FLUX Z_at_0_3
  VERTICES
    4 5 8 7
  /
END

INTEGRAL_FLUX Z_at_0_4
  VERTICES
    5 6 9 8
  /
END

# =============================== Z plane at 2 ================================
INTEGRAL_FLUX
  ! @ 1 mm/s for 2 s = 8 kg total, 4 kg/s
  NAME Z_at_2
  VERTICES
    23 24 27 26
    22 23 26 25
    20 21 24 23
    19 20 23 22
  /
END

! the four below should sum to the above
INTEGRAL_FLUX Z_at_2_5
  VERTICES
    19 20 23 22
  /
END

INTEGRAL_FLUX Z_at_2_6
  VERTICES
    20 21 24 23
  /
END

INTEGRAL_FLUX Z_at_0_7
  VERTICES
    22 23 26 25
  /
END

INTEGRAL_FLUX Z_at_2_8
  VERTICES
    23 24 27 26
  /
END

